commit 0908dd7788dc01d8a7f517393b3662ebd5517199
Author: EddieCueto <cueto303@gmail.com>
Date:   Sun Oct 15 12:36:19 2017 -0500

    Initial commit

diff --git a/.gitattributes b/.gitattributes
new file mode 100644
index 0000000..eba1110
--- /dev/null
+++ b/.gitattributes
@@ -0,0 +1,2 @@
+# Auto detect text files and perform LF normalization
+* text=auto
\ No newline at end of file
diff --git a/.idea/misc.xml b/.idea/misc.xml
new file mode 100644
index 0000000..dc42e37
--- /dev/null
+++ b/.idea/misc.xml
@@ -0,0 +1,4 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectRootManager" version="2" project-jdk-name="Python 3.6.0 (~/.anaconda3/bin/python)" project-jdk-type="Python SDK" />
+</project>
\ No newline at end of file
diff --git a/.idea/modules.xml b/.idea/modules.xml
new file mode 100644
index 0000000..11ca388
--- /dev/null
+++ b/.idea/modules.xml
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/sim_bin_tree.iml" filepath="$PROJECT_DIR$/.idea/sim_bin_tree.iml" />
+    </modules>
+  </component>
+</project>
\ No newline at end of file
diff --git a/.idea/sim_bin_tree.iml b/.idea/sim_bin_tree.iml
new file mode 100644
index 0000000..6f63a63
--- /dev/null
+++ b/.idea/sim_bin_tree.iml
@@ -0,0 +1,12 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<module type="PYTHON_MODULE" version="4">
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="inheritedJdk" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+  <component name="TestRunnerService">
+    <option name="projectConfiguration" value="Nosetests" />
+    <option name="PROJECT_TEST_RUNNER" value="Nosetests" />
+  </component>
+</module>
\ No newline at end of file
diff --git a/.idea/vcs.xml b/.idea/vcs.xml
new file mode 100644
index 0000000..94a25f7
--- /dev/null
+++ b/.idea/vcs.xml
@@ -0,0 +1,6 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="VcsDirectoryMappings">
+    <mapping directory="$PROJECT_DIR$" vcs="Git" />
+  </component>
+</project>
\ No newline at end of file
diff --git a/.idea/workspace.xml b/.idea/workspace.xml
new file mode 100644
index 0000000..dc9ce9c
--- /dev/null
+++ b/.idea/workspace.xml
@@ -0,0 +1,239 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ChangeListManager">
+    <list default="true" id="7b849342-5b10-423b-a282-79b16f319961" name="Default" comment="">
+      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/.idea/vcs.xml" />
+      <change type="MODIFICATION" beforePath="$PROJECT_DIR$/.idea/workspace.xml" afterPath="$PROJECT_DIR$/.idea/workspace.xml" />
+      <change type="MODIFICATION" beforePath="$PROJECT_DIR$/mcBinTree.py" afterPath="$PROJECT_DIR$/mcBinTree.py" />
+    </list>
+    <option name="EXCLUDED_CONVERTED_TO_IGNORED" value="true" />
+    <option name="TRACKING_ENABLED" value="true" />
+    <option name="SHOW_DIALOG" value="false" />
+    <option name="HIGHLIGHT_CONFLICTS" value="true" />
+    <option name="HIGHLIGHT_NON_ACTIVE_CHANGELIST" value="false" />
+    <option name="LAST_RESOLUTION" value="IGNORE" />
+  </component>
+  <component name="FileEditorManager">
+    <leaf SIDE_TABS_SIZE_LIMIT_KEY="300">
+      <file leaf-file-name="makeTree.py" pinned="false" current-in-tab="false">
+        <entry file="file://$PROJECT_DIR$/makeTree.py">
+          <provider selected="true" editor-type-id="text-editor">
+            <state relative-caret-position="0">
+              <caret line="0" column="0" lean-forward="false" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
+              <folding />
+            </state>
+          </provider>
+        </entry>
+      </file>
+      <file leaf-file-name="mcBinTree.py" pinned="false" current-in-tab="true">
+        <entry file="file://$PROJECT_DIR$/mcBinTree.py">
+          <provider selected="true" editor-type-id="text-editor">
+            <state relative-caret-position="225">
+              <caret line="18" column="17" lean-forward="false" selection-start-line="18" selection-start-column="17" selection-end-line="18" selection-end-column="17" />
+              <folding />
+            </state>
+          </provider>
+        </entry>
+      </file>
+      <file leaf-file-name="README.md" pinned="false" current-in-tab="false">
+        <entry file="file://$PROJECT_DIR$/README.md">
+          <provider selected="true" editor-type-id="text-editor">
+            <state relative-caret-position="0">
+              <caret line="0" column="0" lean-forward="false" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
+              <folding />
+            </state>
+          </provider>
+        </entry>
+      </file>
+    </leaf>
+  </component>
+  <component name="Git.Settings">
+    <option name="RECENT_GIT_ROOT_PATH" value="$PROJECT_DIR$" />
+  </component>
+  <component name="IdeDocumentHistory">
+    <option name="CHANGED_PATHS">
+      <list>
+        <option value="$PROJECT_DIR$/mcBinTree.py" />
+      </list>
+    </option>
+  </component>
+  <component name="ProjectFrameBounds">
+    <option name="y" value="23" />
+    <option name="width" value="1440" />
+    <option name="height" value="821" />
+  </component>
+  <component name="ProjectLevelVcsManager" settingsEditedManually="true" />
+  <component name="ProjectView">
+    <navigator currentView="ProjectPane" proportions="" version="1">
+      <flattenPackages />
+      <showMembers />
+      <showModules />
+      <showLibraryContents />
+      <hideEmptyPackages />
+      <abbreviatePackageNames />
+      <autoscrollToSource />
+      <autoscrollFromSource />
+      <sortByType />
+      <manualOrder />
+      <foldersAlwaysOnTop value="true" />
+    </navigator>
+    <panes>
+      <pane id="Scope" />
+      <pane id="Scratches" />
+      <pane id="ProjectPane">
+        <subPane>
+          <expand>
+            <path>
+              <item name="sim_bin_tree" type="b2602c69:ProjectViewProjectNode" />
+              <item name="sim_bin_tree" type="462c0819:PsiDirectoryNode" />
+            </path>
+            <path>
+              <item name="sim_bin_tree" type="b2602c69:ProjectViewProjectNode" />
+              <item name="External Libraries" type="cb654da1:ExternalLibrariesNode" />
+            </path>
+            <path>
+              <item name="sim_bin_tree" type="b2602c69:ProjectViewProjectNode" />
+              <item name="External Libraries" type="cb654da1:ExternalLibrariesNode" />
+              <item name="&lt; Python 3.6.0 (~/.anaconda3/bin/python) &gt;" type="70bed36:NamedLibraryElementNode" />
+            </path>
+          </expand>
+          <select />
+        </subPane>
+      </pane>
+    </panes>
+  </component>
+  <component name="PropertiesComponent">
+    <property name="settings.editor.selected.configurable" value="configurable.group.appearance" />
+    <property name="last_opened_file_path" value="$PROJECT_DIR$" />
+  </component>
+  <component name="RunDashboard">
+    <option name="ruleStates">
+      <list>
+        <RuleState>
+          <option name="name" value="ConfigurationTypeDashboardGroupingRule" />
+        </RuleState>
+        <RuleState>
+          <option name="name" value="StatusDashboardGroupingRule" />
+        </RuleState>
+      </list>
+    </option>
+  </component>
+  <component name="RunManager" selected="Python.mcBinTree">
+    <configuration name="mcBinTree" type="PythonConfigurationType" factoryName="Python" temporary="true">
+      <option name="INTERPRETER_OPTIONS" value="" />
+      <option name="PARENT_ENVS" value="true" />
+      <envs>
+        <env name="PYTHONUNBUFFERED" value="1" />
+      </envs>
+      <option name="SDK_HOME" value="" />
+      <option name="WORKING_DIRECTORY" value="$PROJECT_DIR$" />
+      <option name="IS_MODULE_SDK" value="true" />
+      <option name="ADD_CONTENT_ROOTS" value="true" />
+      <option name="ADD_SOURCE_ROOTS" value="true" />
+      <module name="sim_bin_tree" />
+      <option name="SCRIPT_NAME" value="$PROJECT_DIR$/mcBinTree.py" />
+      <option name="PARAMETERS" value="" />
+      <option name="SHOW_COMMAND_LINE" value="false" />
+      <option name="EMULATE_TERMINAL" value="false" />
+    </configuration>
+    <recent_temporary>
+      <list size="1">
+        <item index="0" class="java.lang.String" itemvalue="Python.mcBinTree" />
+      </list>
+    </recent_temporary>
+  </component>
+  <component name="ShelveChangesManager" show_recycled="false">
+    <option name="remove_strategy" value="false" />
+  </component>
+  <component name="TaskManager">
+    <task active="true" id="Default" summary="Default task">
+      <changelist id="7b849342-5b10-423b-a282-79b16f319961" name="Default" comment="" />
+      <created>1508087209517</created>
+      <option name="number" value="Default" />
+      <option name="presentableId" value="Default" />
+      <updated>1508087209517</updated>
+    </task>
+    <servers />
+  </component>
+  <component name="ToolWindowManager">
+    <frame x="0" y="23" width="1440" height="821" extended-state="0" />
+    <editor active="true" />
+    <layout>
+      <window_info id="Project" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.2532189" sideWeight="0.5" order="0" side_tool="false" content_ui="combo" />
+      <window_info id="TODO" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="6" side_tool="false" content_ui="tabs" />
+      <window_info id="Event Log" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="true" content_ui="tabs" />
+      <window_info id="Run" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.32859176" sideWeight="0.5" order="2" side_tool="false" content_ui="tabs" />
+      <window_info id="Version Control" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="false" content_ui="tabs" />
+      <window_info id="Python Console" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="false" content_ui="tabs" />
+      <window_info id="Structure" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="1" side_tool="false" content_ui="tabs" />
+      <window_info id="Terminal" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="false" content_ui="tabs" />
+      <window_info id="Debug" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.4" sideWeight="0.5" order="3" side_tool="false" content_ui="tabs" />
+      <window_info id="Favorites" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="2" side_tool="true" content_ui="tabs" />
+      <window_info id="Data View" active="false" anchor="right" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="3" side_tool="false" content_ui="tabs" />
+      <window_info id="Cvs" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="4" side_tool="false" content_ui="tabs" />
+      <window_info id="Message" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="0" side_tool="false" content_ui="tabs" />
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+      <window_info id="Ant Build" active="false" anchor="right" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.25" sideWeight="0.5" order="1" side_tool="false" content_ui="tabs" />
+    </layout>
+  </component>
+  <component name="VcsContentAnnotationSettings">
+    <option name="myLimit" value="2678400000" />
+  </component>
+  <component name="XDebuggerManager">
+    <breakpoint-manager />
+    <watches-manager />
+  </component>
+  <component name="editorHistoryManager">
+    <entry file="file://$PROJECT_DIR$/makeTree.py">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="0">
+          <caret line="0" column="0" lean-forward="false" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
+          <folding />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/README.md">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="0">
+          <caret line="0" column="0" lean-forward="false" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
+          <folding />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/mcBinTree.py">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="225">
+          <caret line="18" column="17" lean-forward="false" selection-start-line="18" selection-start-column="17" selection-end-line="18" selection-end-column="17" />
+          <folding />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/README.md">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="0">
+          <caret line="0" column="0" lean-forward="false" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
+          <folding />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/makeTree.py">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="0">
+          <caret line="0" column="0" lean-forward="false" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
+          <folding />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/mcBinTree.py">
+      <provider selected="true" editor-type-id="text-editor">
+        <state relative-caret-position="225">
+          <caret line="18" column="17" lean-forward="false" selection-start-line="18" selection-start-column="17" selection-end-line="18" selection-end-column="17" />
+          <folding />
+        </state>
+      </provider>
+    </entry>
+  </component>
+</project>
\ No newline at end of file
diff --git a/LICENSE b/LICENSE
new file mode 100644
index 0000000..41b94d1
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,674 @@
+GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
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+
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+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    {one line to give the program's name and a brief idea of what it does.}
+    Copyright (C) 2017  {name of author}
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    sim_bin_tree  Copyright (C) 2017  EddieCueto
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.
\ No newline at end of file
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..1202543
--- /dev/null
+++ b/README.md
@@ -0,0 +1 @@
+# sim_bin_tree
diff --git a/__pycache__/makeTree.cpython-36.pyc b/__pycache__/makeTree.cpython-36.pyc
new file mode 100755
index 0000000..ced5fd7
Binary files /dev/null and b/__pycache__/makeTree.cpython-36.pyc differ
diff --git a/__pycache__/mcMatrix.cpython-36.pyc b/__pycache__/mcMatrix.cpython-36.pyc
new file mode 100755
index 0000000..00a1513
Binary files /dev/null and b/__pycache__/mcMatrix.cpython-36.pyc differ
diff --git a/__pycache__/totalVariationNorm.cpython-36.pyc b/__pycache__/totalVariationNorm.cpython-36.pyc
new file mode 100755
index 0000000..5756c9a
Binary files /dev/null and b/__pycache__/totalVariationNorm.cpython-36.pyc differ
diff --git a/makeTree.py b/makeTree.py
new file mode 100755
index 0000000..fb1fc22
--- /dev/null
+++ b/makeTree.py
@@ -0,0 +1,164 @@
+#!/usr/bin/env python2
+# -*- coding: utf-8 -*-
+"""
+Created on Sat May  6 16:14:29 2017
+This function creates a Tree given a depth and an optional arity.
+The output can be the set of vertex and edges, or the adjacency 
+matrix of the tree.
+@author: eddie
+"""
+
+try:
+    def tree(depth,n_arity=2,matrix=False,self_loop = False):
+        import numpy as np
+        import math as mt
+        
+        if (n_arity >= 2) and (depth > 1):  # this checks the depth and arity of the tree
+            E = []
+            i = 0
+            n = int((mt.pow(n_arity,depth) - 1)/(n_arity - 1))  # number of vertex in the tree
+            for r in range(0,n_arity,n_arity):  # this for builds the edges of the tree 
+                i=0
+                for j in range(1,n):
+                    E.append((i,j))
+                    if (np.mod(j,n_arity)) == 0:
+                        i+=1
+                                
+            if (matrix == False) and (self_loop == True):
+                for r in range(0,n):
+                    E.append((r,r))
+                    
+                G = []
+                V = []
+                
+                for v in range(n):
+                    V.append(v)
+                        
+                G = [V, sorted(E)]
+                return G
+        
+            if (matrix == True) and (self_loop == True):
+                G = []
+                for v in E:
+                    G.append(tuple(sorted(v,reverse=True)))
+                
+                E = E + G
+                for r in range(0,n):
+                    E.append((r,r))
+                
+                R = np.zeros((n,n))
+                for v in E:
+                    R[v] = 1
+
+                return R
+        
+            if (matrix == False) and (self_loop == False):
+                G = []
+                V = []
+                for v in range(n):
+                    V.append(v)
+                    
+                G = [V, E]
+                return G
+            else:
+                G = []
+                for v in E:
+                    G.append(tuple(sorted(v,reverse=True)))
+
+                E = E + G
+                R = np.zeros((n,n))
+                
+                for v in E:
+                    R[v] = 1
+
+                return R
+        if depth == 1:
+            V = [0]
+            E = []
+            
+            if (matrix == True) and (self_loop == False):
+                print('This option is not available whith depth 1 and no loop')
+                
+            if (matrix == True) and (self_loop == True):
+                R = np.zeros((1,1))
+                R[0,0] = 1
+                return R
+            
+            if (matrix == False) and (self_loop == True):
+                E = [(0,0)]
+                G = [V,E]
+                
+                return G
+            
+            G = [V,E]
+            return G
+        
+        if n_arity == 1 and depth > 1:
+            E = []
+            n = depth
+            for i in range(0,n-1):
+                E.append((i,i+1))
+            
+            if (matrix == False) and (self_loop == True):
+                for r in range(0,n):
+                    E.append((r,r))
+                    
+                G = []
+                V = []
+                
+                for v in range(n):
+                    V.append(v)
+                    
+                G = [V, sorted(E)]
+                return G
+        
+            if (matrix == True) and (self_loop == True):
+                G = []
+                for v in E:
+                    G.append(tuple(sorted(v,reverse=True)))
+                
+                E = E + G
+                
+                for r in range(0,n):
+                    E.append((r,r))
+                
+                R = np.zeros((n,n))
+                
+                for v in E:
+                    R[v] = 1
+
+                return R
+        
+            if (matrix == False) and (self_loop == False):
+                G = []
+                V = []
+                
+                for v in range(n):
+                    V.append(v)
+                    
+                G = [V, E]
+                return G
+            else:
+                G = []
+                
+                for v in E:
+                    G.append(tuple(sorted(v,reverse=True)))
+
+                E = E + G
+                R = np.zeros((n,n))
+                
+                for v in E:
+                    R[v] = 1
+
+                return R
+            
+        if (n_arity < 1) or (depth < 1):
+            print('There is no tree with this properties!!!')
+        
+except IndexError:
+    print('error!')
+
+T = tree(3,2,False, True)
+
+
+        
\ No newline at end of file
diff --git a/makeTree.pyc b/makeTree.pyc
new file mode 100755
index 0000000..470cdcc
Binary files /dev/null and b/makeTree.pyc differ
diff --git a/mcBinTree.py b/mcBinTree.py
new file mode 100755
index 0000000..2fe6a9b
--- /dev/null
+++ b/mcBinTree.py
@@ -0,0 +1,116 @@
+# -*- coding: utf-8 -*-
+"""
+Simulation of a random walk on a finite b-ary tree of depth k
+
+"""
+
+import random as rn
+import numpy as np
+import matplotlib.pyplot as plt
+import math as mt
+
+rn.seed(666)
+
+k = 20 # depth of the tree
+b = 2 # arity of the tree
+T = 100 # number of steps taken by the MC
+exp = 100000 # repetition of experiments
+
+E = np.zeros(exp)
+M = np.zeros(exp)
+
+for b in range(0,exp):
+    X = np.zeros(T)
+    Y = np.zeros(T)
+    Z = np.zeros(T)
+
+    for a in range(0, T):
+        Z[a] = T
+
+    X[0] = rn.randint(0,k) # setting the starting level for X
+    Y[0] = rn.randint(0,k) # setting the starting level for Y
+
+    for a in range(0, (T - 1)):
+        monX = rn.randint(0,1)
+        probArisX = rn.randint(0,(b + 1)) 
+        monY = rn.randint(0,1)
+        probArisY = rn.randint(0,(b + 1)) 
+        if X[a] != Y[a]:
+            if X[a] > 0 and X[a] < k:
+                if monX == 1: 
+                    X[a + 1] = X[a]
+                if monX == 0: 
+                    if probArisX == 0:
+                        X[a + 1] = (X[a] - 1)
+                    if probArisX != 0:
+                        X[a + 1] = (X[a] + 1)
+            if X[a] == 0:
+                if monX == 1: 
+                    X[a + 1] = 0
+                if monX == 0:
+                    X[a + 1] = 1
+            if X[a] == k:
+                if monX == 1: 
+                    X[a + 1] = k
+                if monX == 0:
+                    X[a + 1] = (k - 1)
+            if Y[a] > 0 and Y[a] < k:
+                if monY == 1: 
+                    Y[a + 1] = Y[a]
+                if monY == 0: 
+                    if probArisY == 0:
+                        Y[a + 1] = (Y[a] - 1)
+                    if probArisY != 0:
+                        Y[a + 1] = (Y[a] + 1)
+            if Y[a] == 0:
+                if monY == 1: 
+                    Y[a + 1] = 0
+                if monY == 0:
+                    Y[a + 1] = 1
+            if Y[a] == k:
+                if monY == 1: 
+                    Y[a + 1] = k
+                if monY == 0:
+                    Y[a + 1] = (k - 1)
+        if X[a] == Y[a]:
+            Z[a] = a
+            if X[a] > 0 and X[a] < k:
+                if monX == 1: 
+                    X[a + 1] = X[a]
+                    Y[a + 1] = X[a + 1]
+                if monX == 0: 
+                    if probArisX == 0:
+                        X[a + 1] = (X[a] - 1)
+                        Y[a + 1] = X[a + 1]
+                    if probArisX != 0:
+                        X[a + 1] = (X[a] + 1)
+                        Y[a + 1] = X[a + 1]
+            if X[a] == 0:
+                if monX == 1: 
+                    X[a + 1] = 0
+                    Y[a + 1] = X[a + 1]
+                if monX == 0:
+                    X[a + 1] = 1
+                    Y[a + 1] = X[a + 1]
+            if X[a] == k:
+                if monX == 1: 
+                    X[a + 1] = k
+                    Y[a + 1] = X[a + 1]
+                if monX == 0:
+                    X[a + 1] = (k - 1)
+                    Y[a + 1] = X[a + 1]
+    E[b] = np.amin(Z)
+    
+m = np.mean(E)   
+for b in range(0,exp):
+    M[b] = m
+    
+n = (mt.pow(b,k + 1) - 1)/(b - 1)
+#plt.hist(E,histtype='bar')
+
+plt.plot(E,'bo',ms=0.8)
+plt.plot(M, 'r')
+plt.show()
+
+#if m <= 4*n:
+#    print('Test passed')
\ No newline at end of file
diff --git a/mcMatrix.py b/mcMatrix.py
new file mode 100755
index 0000000..721e591
--- /dev/null
+++ b/mcMatrix.py
@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Sat May  6 16:20:10 2017
+A matrix of a Markov Chain is creatated
+@author: eddie
+"""
+
+def markovTreeMatrix(depth, arity=2, lazy=False):
+    from makeTree import tree
+    import numpy as np
+    import math as mt
+    
+    if lazy == True:
+        T = tree(depth, arity)
+        G = []
+        for v in T[1]:
+            G.append(tuple(sorted(v,reverse=True)))
+        #for v in T[0]:
+        #    G.append((v,v))
+            
+        G = T[1] + G
+        G = sorted(G)
+        
+        nodes = mt.pow(arity,depth - 1) - 1  # this is the first leaf
+        
+        n = len(T[0])
+        
+        R = np.zeros((n,n))  # we define a zeros matrix
+        
+        for x in G:
+            if x[0] == 0:
+                R[x] = (1/arity)  # the probability of moving from the root
+                
+            if x[0] > 0 and x[1] >= nodes:
+                R[x] = (1/(arity + 1))  # the probability of moving from middle nodes
+            
+            if x[0] >= nodes:
+                R[x] = 1  # the probability of moving from a leaf
+                
+        for y in G:
+            if R[y] == 0:
+                R[y] = (1/(arity + 1))
+                
+        E = []
+
+        for m in range(0,len(R)):
+            E.append((m,m))
+    
+        for z in E:
+            R[z] = (1/2)
+            
+        #R = (1/2)*R  # this is lazy because we have 0.5 probability of not moving from our node
+                        
+        return R
+    
+    else:
+        T = tree(depth, arity)
+        G = []
+        for v in T[1]:
+            G.append(tuple(sorted(v,reverse=True)))
+            
+        G = T[1] + G
+        
+        nodes = mt.pow(arity,depth - 1) - 1
+        
+        n = len(T[0])
+        
+        R = np.zeros((n,n))
+        
+        for x in G:
+            if x[0] == 0:
+                R[x] = (1/arity)
+                
+            if x[0] > 0 and x[1] >= nodes:
+                R[x] = (1/(arity + 1))
+            
+            if x[0] >= nodes:
+                R[x] = 1
+                
+        for y in G:
+            if R[y] == 0:
+                R[y] = (1/(arity + 1))
+            
+        return R
+        
+T = markovTreeMatrix(5,2,False)
\ No newline at end of file
diff --git a/mcSim.py b/mcSim.py
new file mode 100755
index 0000000..90432ae
--- /dev/null
+++ b/mcSim.py
@@ -0,0 +1,41 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Mon May  8 16:02:18 2017
+
+@author: eddie
+"""
+
+from mcMatrix import markovTreeMatrix as mc
+from totalVariationNorm import totalVariation1 as TV
+import numpy as np
+import matplotlib.patches as mpatches
+import matplotlib.pyplot as plt
+
+np.random.seed(666)
+
+arity = 2  # arity of tree
+depth = 3  # depth of tree
+
+P = mc(depth,arity)  # mc(depth of tree, arity of tree 2 by default)
+
+pi = np.random.randn(len(P))  # the initial randomly generated vector, to show
+                              # that in fact pi will converge to stationary.
+
+stat = []
+for x in range(0,len(P)):  # uniform distribution of the tree
+    stat.append(1/arity)
+
+
+
+near = []
+
+for x in range(100):
+    pi = P.dot(pi)
+    near.append(TV(pi,stat))
+    
+    
+red_patch = mpatches.Patch(color='red', label='TV convergence to stationary dist')
+plt.legend(handles=[red_patch])    
+plt.plot(near,'ro', ms='0.8')
+plt.show()
\ No newline at end of file
diff --git a/oneRunMC.py b/oneRunMC.py
new file mode 100755
index 0000000..ed5b984
--- /dev/null
+++ b/oneRunMC.py
@@ -0,0 +1,118 @@
+#!/usr/bin/env python2
+# -*- coding: utf-8 -*-
+"""
+Simulation of a random walk on a finite b-ary tree of depth k
+
+"""
+
+import random as rn
+import numpy as np
+import matplotlib.pyplot as plt
+#import math as mt
+
+#rn.seed(666)
+
+k = 10  # depth of the tree
+b = 2  # arity of the tree
+T = 100  # number of steps taken by the MC
+
+X = np.zeros(T)
+Y = np.zeros(T)
+Z = np.zeros(T)
+
+for a in range(0, T):
+    Z[a] = T
+
+X[0] = rn.randint(0,k)  # setting the starting level for X
+Y[0] = rn.randint(0,k)  # setting the starting level for Y
+
+for a in range(0, (T - 1)):
+    monX = rn.randint(0,1)
+    probArisX = rn.randint(0,(b + 1)) 
+    monY = rn.randint(0,1)
+    probArisY = rn.randint(0,(b + 1)) 
+    if X[a] != Y[a]:  # if X is different to Y
+        if X[a] > 0 and X[a] < k:  # if the MC is in the middle depths of the tree
+            if monX == 1: 
+                X[a + 1] = X[a]
+            if monX == 0: 
+                if probArisX == 0:
+                    X[a + 1] = (X[a] - 1)
+                if probArisX != 0:
+                    X[a + 1] = (X[a] + 1)
+        if X[a] == 0:  # if the MC is in the root node
+            if monX == 1: 
+                X[a + 1] = X[a]
+            if monX == 0:
+                X[a + 1] = (X[a] + 1)
+        if X[a] == k:  # if the MC is in the leaf of the tree
+            if monX == 1: 
+                X[a + 1] = X[a]
+            if monX == 0:
+                X[a + 1] = (X[a] - 1)
+        if Y[a] > 0 and Y[a] < k:  
+            if monY == 1: 
+                Y[a + 1] = Y[a]
+            if monY == 0: 
+                if probArisY == 0:
+                    Y[a + 1] = (Y[a] - 1)
+                if probArisY != 0:
+                    Y[a + 1] = (Y[a] + 1)
+        if Y[a] == 0:
+            if monY == 1: 
+                Y[a + 1] = Y[a]
+            if monY == 0:
+                Y[a + 1] = (Y[a] + 1)
+        if Y[a] == k:
+            if monY == 1: 
+                Y[a + 1] = Y[a]
+            if monY == 0:
+                Y[a + 1] = (Y[a] - 1)
+    
+    if X[a] == Y[a]:  # if X is equal to Y
+        Z[a] = a
+        if X[a] > 0 and X[a] < k:
+            if monX == 1: 
+                X[a + 1] = X[a]
+                Y[a + 1] = X[a]  #X[a + 1]
+            if monX == 0: 
+                if probArisX == 0:
+                    X[a + 1] = (X[a] - 1)
+                    Y[a + 1] = (X[a] - 1)  #X[a + 1]
+                if probArisX != 0:
+                    X[a + 1] = (X[a] + 1)
+                    Y[a + 1] = (X[a] + 1)  #X[a + 1]
+        if X[a] == 0:
+            if monX == 1: 
+                X[a + 1] = X[a]
+                Y[a + 1] = X[a]  #X[a + 1]
+            if monX == 0:
+                X[a + 1] = (X[a] + 1)
+                Y[a + 1] = (X[a] + 1)  #X[a + 1]
+                    
+        if X[a] == k:
+            if monX == 1: 
+                X[a + 1] = X[a]
+                Y[a + 1] = X[a]  #X[a + 1]
+            if monX != 1:
+                X[a + 1] = (X[a] - 1)
+                Y[a + 1] = (X[a] - 1)  #X[a + 1]
+                    
+                      
+#plt.plot(X,'ro',ms=0.8)
+#plt.plot(Y,'bo',ms=0.8)
+plt.plot(X,'r')
+plt.plot(Y,'b')
+plt.show()                
+                
+t = np.amin(Z)                  
+print("t_cou = " + str(t))
+
+#n = (mt.pow(b,k + 1) - 1)/(b - 1)  # number of vertex in the tree T_{b,k}  b - arity, k - depth
+
+#if t != 0:
+#    if t <= ((4 * n)/T):
+#        print("The test is passed")
+#else:
+#    print("The MC started coupled")
+
diff --git a/totalVariationNorm.py b/totalVariationNorm.py
new file mode 100755
index 0000000..b99a049
--- /dev/null
+++ b/totalVariationNorm.py
@@ -0,0 +1,66 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+
+The total variation Norm
+
+"""
+
+def checkVectors(distrib_1,distrib_2):
+    import numpy as np
+    
+    mu = np.asarray(distrib_1)
+    nu = np.asarray(distrib_2)
+    mu_sum = np.sum(mu)
+    nu_sum = np.sum(nu)
+    mu_chk = (mu >= 0)
+    nu_chk = (nu >= 0)
+        
+    if mu.size != nu.size:
+        print('vectors of diferent length')
+        return False
+        
+    else:
+        if (mu_sum != 1) or (nu_sum != 1):
+           #print('one of the vectors is not a probability distribution')
+            return False
+        else:
+            if (mu_chk.all() != True) or (nu_chk.all() != True):
+                #print('one of the vectors is not a probability distribution')
+                return False
+            else:
+                if mu.shape != nu.shape:
+                    return True
+                    
+        
+def totalVariation1(distrib_1,distrib_2):
+    import numpy as np
+    
+    if checkVectors(distrib_1,distrib_2) == False:
+        mu = np.asarray(distrib_1)
+        nu = np.asarray(distrib_2)
+        
+        return np.max(np.abs(mu - nu))
+        
+    else:
+        print('Not possible to calculate measure of the vectors')
+        
+        
+def totalVariation2(distrib_1,distrib_2):
+    import numpy as np
+    
+    if checkVectors(distrib_1,distrib_2) == True:
+        mu = np.asarray(distrib_1)
+        nu = np.asarray(distrib_2)
+        temp = []
+    
+        for x in range(0,nu.size):
+            temp.append(np.abs(mu[x] - nu[x]))
+        
+        temp = np.asarray(temp)
+        
+        return (0.5)*temp.sum()
+        
+    else:
+        print('Not possible to calculate measure of the vectors')       
+    
\ No newline at end of file